Given $ m \angle RPS = 8x + 120$, and $ m \angle QPR = 2x + 50$, find $m\angle RPS$. $P$ $Q$ $S$ $R$
Solution: From the diagram, we see that together ${\angle QPR}$ and ${\angle RPS}$ form ${\angle QPS}$ , so $ {m\angle QPR} + {m\angle RPS} = {m\angle QPS}$ Since $\angle QPS$ is a straight angle, we know ${m\angle QPS = 180}$ Substitute in the expressions that were given for each measure: $ {2x + 50} + {8x + 120} = {180}$ Combine like terms: $ 10x + 170 = 180$ Subtract $170$ from both sides: $ 10x = 10$ Divide both sides by $10$ to find $x$ $ x = 1$ Substitute $1$ for $x$ in the expression that was given for $m\angle RPS$ $ m\angle RPS = 8({1}) + 120$ Simplify: $ {m\angle RPS = 8 + 120}$ So ${m\angle RPS = 128}$.